Gas Laws Involving Temperature

A few initial inquiries to start off with... How do balloonists prepare their balloons for take-off? Why do tires on a car sometimes seem flat and sometimes seem full? How does a pressure cooker work?

What happens when a gas is heated? At a higher temperature, gas molecules move faster. They collide with the walls of the container more frequently and with greater force. The increased pressure causes the volume of a flexible container to increase; then the molecules must travel farther before reaching the walls, so the rate of collisions decreases. So even though the collisions have more force, they become less frequent, so the pressure stays constant. Thus, temperature increases, volume increases, but pressure remains the same.

An Illustration of Charles's Law

Graphing Volume vs. Temperature Using temperature as the x-axis and volume as the y-axis, the resulting plot is a straight line, indicating that as the temperature of a gas increases, its volume increases. At absolute zero, that is, at -273 degrees Celsius or O Kelvin, the kinetic energy of particles is zero, so all motion of gas particles ceases at that point. Most real gases cannot be cooled to absolute zero because they condense to form liquids or solids due to intermolecular forces.

A Graph of Volume vs. Kelvin Temperature

The Beauty of the Kelvin Scale The average kinetic energy of gas molecules is more closely related to the Kelvin temperature. Gas volume and Kelvin temperature are directly proportional to each other. For example, quadrupling the Kelvin temperature causes the volume of the gas to quadruple. Reducing the temperature by half causes the volume of gas to decrease by half. This leads us to Charles's law.

It may be expressed mathematically as: Charles's law: States that the volume of a given mass of gas is directly proportional to its kelvin temperature at constant pressure. It may be expressed mathematically as: V = kT or V/T = k where V is the volume, T is the Kelvin temperature, and k is a constant. The value of k depends on the quantity of gas and the pressure.

Applying Charles's Law When comparing two sets of conditions (e.g. initial and final), we can express Charles's law with the equation on the right. If we know 3 of the values, we can solve for the 4th value.

Charles's Law Practice Problems 1. A sample of neon gas occupies a volume of 752 mL at 25 deg. C. What volume will the gas occupy at 50 deg. C if the pressure remains constant? 2. A gas at 65 deg. C occupies 4.22 L. At what Celsius temperature will the volume be 3.87 L, assuming the same pressure?

An Application of Charles's Law In the first step of a chemical explosion, chemicals react with each other to produce gaseous products. For example, when black gunpowder is ignited, potassium nitrate, sulfur, and charcoal react to form four gases- - carbon monoxide, carbon dioxide, sulfur dioxide, and nitric oxide-- along with solid side products. A great deal of heat is released in the reaction, causing the gases formed to expand rapidly, producing the shock wave that is characteristic of explosions.

What is the relationship between a gas's temperature and pressure? Joseph Gay-Lussac found that a direct relationship exists between the kelvin temperature and the pressure of a gas. If we increase temperature but keep volume constant, the energy and frequency of the gas molecules will increase, causing pressure to build up on the walls of the container.

Gay-Lussac's law: States that the pressure of a given mass of gas varies directly with the kelvin temperature when the volume remains constant. We may express it mathematically as: P = kT or P/T = k where P is the pressure, T is the Kelvin temperature, and k is a constant. The value of k depends on the quantity of gas and the volume.

Applying Gay-Lussac's Law When comparing two sets of conditions (e.g. initial and final), we can express Gay- Lussac's law with the equation on the right. If we know 3 of the values, we can solve for the 4th value.

Gay-Lussac's Law Practice Problems 1. On a hot August day, before James's trip from Loudon to Cookeville, the pressure in his car's tires is 1.8 atm at 21 deg C. At the end of the trip, the pressure gauge reads 1.9 atm. What is the new Celsius temperature of the air inside the tires (assuming they have constant volume)? 2. At 121 deg. C, the pressure of a sample of nitrogen is 108 kPa. What will the pressure be at 205 deg. C, (assuming constant volume)?